The Benefits of Extended Liability∗

Yolande Hiriart† and David Martimort‡

This Version: June 14, 2005

Abstract: We characterize the optimal regulation of a firm which undertakes an

environmentally risky activity. This firm (the agent) is protected by limited liability and

bound by contract to a stakeholder (the principal). A key feature is the non-observability

of the level of safety care exerted by the agent. This level of care depends both on the

degree of incompleteness of the regulatory contract (i.e., whether private transactions can

be controlled or not) and on the allocation of bargaining power between the principal and

the agent. Increasing the wealth of the principal that can be seized upon an accident has no

value when private transactions are regulated but might strictly improve welfare otherwise.

We derive bounds on the principal’s wealth so that the second-best complete regulatory

outcome can still be achieved with an incomplete regulation if it is supplemented by an

ex post extended liability regime. Extensions to the cases of multiple principals and of a

ban on regulatory rewards are also analyzed.

∗Financial support by the French Ministry of Ecology and Sustainable Development is acknowledged.We are indebted to the editor Joseph Harrington and to two referees for useful comments which havemuch improved the presentation of the paper. We also thank for comments Denis Gromb and audiencesat various seminars and conferences.†Universite de Toulouse (IDEI, LERNA).‡Universite de Toulouse (IDEI, GREMAQ) and Institut Universitaire de France.

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1 Introduction

Extending liability towards deep-pocket stakeholders of firms engaged in environmentally

risky activities has been a major building block of recent legislations towards environmen-

tal accidents. For instance, under the U.S. 1980 Comprehensive Environmental Response,

Compensation, Liability Act (CERCLA), any owner or operator of an environmentally

risky venture may be found liable for the losses generated by the firm’s activity if the latter

is itself judgment-proof, i.e., if its assets cannot cover the cleanup costs of contaminated

sites.1 Despite the international tendency towards strict liability for environmental harm,

a general agreement on the rationale for relying on liability rules is still missing.2 Extend-

ing liability towards stakeholders has often been viewed as a successful legal response to

finance the remediation of hazardous sites or to indemnify victims (a compensation role).

Common sense suggests that it might also foster incentives for prevention by inducing

private actors to internalize the environmental concerns of the rest of society (an incen-

tive role). This legal doctrine has nevertheless encountered fierce opposition both among

practitioners and scholars. Opponents argue that the benefits of extending liability also

come with some costs. On top of the administrative costs of litigation, extended liability

might change transactions between risky ventures and their contracting partners. Market

structures could be modified accordingly.

This paper gives some theoretical foundations for using a regime of extended liability

and, more broadly, analyze how private transactions between principals and their agents

are modified accordingly. The key justification for doing so is the incompleteness of the

regulation. Indeed, the contracts linking the firm to various stakeholders might affect the

level of care chosen by the firm and thus impact on the environment. These contracts

should thus be regulated in one way or the other. We show in this paper that, even when

no such regulation is possible, the threat of extended liability might induce private actors

to internalize environmental concerns and design private transactions accordingly.

Designing a complete regulation may be of a tantamount difficulty when the set of

partners who contract with the firm performing some hazardous activities and who can

1CERCLA Section 107 (a) casts an extremely broad net in defining those persons that can be liablefor the costs of responding to a release of hazardous substances: current or former owners or operators ofthe facility or vessel, those who arranged for treatment or disposal of hazardous substances at a facility,the transporters of the hazardous substances, and more generally anyone involved in the management ofhazardous substances. Several cases have illustrated this legal doctrine. In the 1986 U.S. v. MarylandBank and Trust case, for instance, a bank was found liable for cleanup costs as an effective “owner” of thefacility at the time the pollution was discovered. More generally, the deep pocket of creditors and otherstakeholders has been requested when such partners were contractually tied with judgment-proof firmsand involved in a sufficiently close relationship. Strasser and Rodosevich (1993) offer a nice perspective onthe principles governing the interpretation of CERCLA. Boyer and Laffont (1996) review the Canadian,the American and the European legal frameworks.

2See Faure and Skogh (2003), Chapters 14 and 17.

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therefore influence the management of environmental risk is not clearly defined at the

design stage.3 Even if the relevant stakeholders can be found out ex ante, environmental

regulators generally do not have the statutory or the auditing rights, or even the expertise,

to control the contracts which bind those stakeholders to the firm’s management.4 The

regulation of environmental risk in such a context is thus necessarily highly incomplete and

leaves these contracts by large uncontrolled. As a result, these contracts may influence care

taking in ways which are detrimental to social welfare. Because of this incompleteness,

relying ex post on liability might improve welfare by putting the various stakeholders of

the firm under the threat of being sanctioned for having wrongly distorted the firm’s care

taking if a bad environmental performance occurs.

We determine circumstances under which an incomplete regulation can be improved by

ex post liability rules. We start with a bare boned model of a vertical relationship between

an agent who is subject to environmental risk regulation and liability, and his principal.

We first characterize the optimal complete regulation in a moral hazard framework where

the agent’s level of safety care is non-verifiable but the transaction between the principal

and this agent can be controlled. Moral hazard and limited liability5 force the regulator

to leave a socially costly rent to the agent to induce care. Reducing this rent requires a

downward distortion of the level care below the first-best.

When the transaction is itself non-verifiable, the regulatory contract is incomplete.

This incompleteness may increase significantly the social costs of inducing safety care.

To the rent left to the agent to induce care, one must now also add the rent left to his

principal so that he designs a private transaction which does not undermine care taking.

Increasing the amount of wealth collectable from the principal under a liability regime

helps nevertheless reducing these extra agency costs. Extended liability may be a rough

substitute for a more complete regulation.

To understand more precisely how this substitution works, note that the regulator faces

two different moral hazard problems. First, he must induce the cashless agent to exert

the proper level of prevention. Second, the regulator must also ensure that the private

transaction linking the principal and the agent does not interfere with the regulatory

incentives for safety care. If this transaction was regulated, these two problems could be

addressed separately. First, the regulator could force the principal to make a payment for

the agent’s services independent on his environmental performances. Private transactions

3For instance, it is often argued that one major problem faced by the Environmental Protection Agencyregulators when enforcing the Resource Conservation and Recovery Act (RCRA) for underground storagetanks is that owners are often difficult to locate.

4As an example, Boyd (2001, p.21) notes that “corporate financial auditing is not a traditional strengthof environmental regulation”.

5Environmentally risky firms are often small in scale since they conceal assets in order to be insulatedfrom the threat of paying for damages. See Ringleb and Wiggins (1990).

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would thus not affect care taking. Second, the regulator could design a convenient set

of regulatory rewards and punishments to induce the agent to exert care. Extending the

principal’s liability would then be useless since, de facto, the principal would not interfere

with the agent’s management of environmental risk.

When private transactions cannot be regulated and a regime of extended liability is

used, the principal is concerned with the agent’s environmental performances since he

may be prosecuted to pay fines following an accident. Part of the benefits from private

contracting may be dissipated through these fines. Private contracting is modified accord-

ingly. This is where the distribution of bargaining power in private contracting matters.

The higher the principal’s bargaining power, the less he will be prone to leave the rent that

a cash-constrained agent must receive to exert care. Private contracts are thus designed

with an eye on reducing this rent. This calls for reducing the level of care performed by

the agent. The unregulated design of private contracting thwarts regulatory incentives.

Anticipating this countervailing effect, an incomplete regulation must induce the prin-

cipal to design a private contract which gives to the agent the correct incentives for safety

care. This can be done by increasing sufficiently fines through a liability regime. However

the principal’s wealth may not suffice to cover large fines. We characterize a lower bound

on the principal’s wealth above which the incompleteness of the regulation does not hurt

if extended liability is also used. Below this bound, one reaches a third-best outcome

characterized by significant care distortions. The principal can still be induced to choose

the right private transaction from a social viewpoint but he must also receive a rent to

do so. The rents left to both the principal and the agent compound and the social cost

of inducing care increases. As a result, the downward distortion in care is exacerbated.

When the agent has most of the bargaining power, he can reap most of the surplus

from the transaction with his principal. When this surplus is independent of the agent’s

environmental performances, contracting has no impact on care taking. Increasing the

principal’s wealth at stake is then useless. More generally, there is a positive relationship

between the wealth needed from a principal to induce care and his bargaining power.

Our paper belongs to a burgeoning literature starting with Pitchford (1995), Heyes

(1996) and Boyer and Laffont (1997) who focus on the relationship between a firm and

its financiers. Those papers argue that extending liability towards fund providers of risky

ventures may not be a panacea. In Pitchford (1995), the competitive financier can only

recoup his financial loss in the event of an accident by asking for higher repayments when

no accident occurs. This depresses the agent’s incentives for exerting safety care. Boyer

and Laffont (1997) argue that increasing the financiers’ liability can deter participation to

projects which are socially valuable. Heyes (1996) shows that increasing liability changes

the pool of loan applicants. Earlier critics have shown that extending liability and putting

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more of the financiers’ wealth at stake recovers some value when principals have most

of the bargaining power (Balkenborg (2001)) or when the damage technology is more

complex than the binary accident-no accident technology used by Pitchford (1995) (Lewis

and Sappington (2001a)). These contributions detail how optimal private contracting

reacts to liability rules. However, the regulatory response to private contracting discussed

there is quite trivial since regulators are concerned only with efficiency and not with rent

extraction.6 In addition, since the only public policies which are available consist of ex

post liability rules, it is hard to figure out whether the cost of extending liability comes

from this restriction or from some more fundamental economic phenomenon. Instead,

we explore optimal regulatory policies when the rents accruing to the private sector are

socially costly. In full generality, a regulatory contract policy should involve both fines if

an accident occurs and rewards if good environmental performances are observed. This

normative approach highlights how agency costs compound when the regulator does not

control private transactions. It allows us to characterize conditions on the principal’s

wealth under which the incompleteness of the regulatory contract can be circumvented.

Section 2 presents the model. Section 3 characterizes the optimal regulation when

moral hazard on safety care is the only issue. The transaction between the principal and

the agent can be fully observed and controlled. In Section 4, we relax this assumption and

explore the optimal regulatory policy and its dependence on the allocation of bargaining

power between the principal and the agent. In Section 5, we extend the analysis to the

case of multiple principals and discuss the case of an institutional constraint banning

regulatory rewards. Section 6 concludes. Proofs are relegated to an Appendix.

2 Model

A cashless firm (the agent) exerts an activity that may provoke an accident harming third-

parties and/or the environment. This agent is bound by contract to a stakeholder (the

principal). The agent’s services generate a surplus Π on behalf of the principal.7 There is a

whole range of activities for which our analysis is relevant. For instance, the agent could

run underground storage tanks or disposal facilities on behalf of parent firms, dispose

wastes collected from clients, or transport hazardous substances on behalf of producers.

A financier could also provide capital to the firm in which case Π would be the net value

of the agent’s project. We should already stress that these different kinds of principals

may significantly differ in terms of their available wealth.

The firm’s activity being risky, an environmental harm D may occur with probability

6A noticeable exception is Boyer and Laffont (1997).7See Boyd and Ingberman (1997) for an earlier model keeping this degree of generality.

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1 − e. The probability that no accident occurs e is normalized so that it is equal to the

agent’s level of safety care (or effort). To exert such an effort, the agent incurs a non-

monetary cost ψ(e). For technical reasons, we assume that ψ′ > 0, ψ′′ > 0, and ψ′′′ > 0

and that the Inada conditions ψ′(0) = 0 and ψ′(1) = +∞ hold so that effort is always

interior.This effort is not observed neither by the principal nor the regulator.

Without loss of generality, a regulatory scheme stipulates payments za and zn to the

agent depending on whether an accident occurs or not. Such a scheme can, for instance,

be understood as resulting from the use of ex post liability following a damage (a fine

−za > 0 imposed on the agent if he has enough earnings from the principal’s contract,

and on the principal if liability is extended) and of an incentive reward (zn > 0) following

good environmental performances. Indeed, since the agent has no cash to indemnify

harmed third-parties, the principal’s contribution may be needed following a damage

if the requested fine is too large and cannot be paid by the agent out of the earnings

he made from contracting with the principal. Even though they do not a priori target

the principal, fines that cannot be paid by the cashless agent end up being paid by

the principal if liability is extended and the principal is himself wealthy enough. Since

private transactions can undo any allocation of liabilities, it does not really matter who

originally bears the fine. This Equivalence Principle is now well-known from the earlier

works of Newman and Wright (1990) and Segerson and Tietenberg (1992) and will be

used at several places below. In particular, we will argue that the incompleteness of

the regulatory contract calls for increasing the fines imposed on the principal/agent pair.

With the Equivalence Principle in mind, such an increase in fines can be reinterpreted as

relying more on extended liability.

Although our modeling uses the direct monetary nature of rewards and punishments,

broader interpretations are available. Bad environmental performances sometimes come

also with damages to the fixed capital of the firm and to some stakeholders (like workers).

Cost may also be indirect: future regulations might be tightened, environmental audits

may be more frequent in the future, the government may refuse authorizations and permits

or raises taxes. Rewards may also stem from the firm’s gains in reputation vis-a-vis its

customers, the government, shareholders and the financial community.8, 9

Denoting by (yn, ya) the payments made by the principal to the agent in each state of

nature, we can rewrite the agent’s expected payoff as:

U = e(zn + yn) + (1− e)(za + ya)− ψ(e).

8On the indirect costs and benefits of a good management of environmental risks, see Lesourd andSchilizzi (2001).

9Those non-monetary transfers may also be socially costly. For instance, reputation gains may alsocreate switching costs in the relationship between the firm and some of its contractual partners. Similarly,tightening future regulations may reduce entry.

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The risk-neutral principal’s net benefit from the transaction is thus given by:

V = Π− eyn − (1− e)ya.

Since the agent has no cash, what really matters from the regulator’s viewpoint is the

wealth w collectable from the principal. We will study how the regulatory outcomes and

the level of safety care may change with w and ask under which circumstances putting

more of the principal’s wealth at stake improves welfare. Of course, the principal can

engage in a variety of strategies to hide the true value of his assets (accounting manipu-

lations, “flight-by-night” techniques, creating cashless subsidiaries, etc...). We will thus

view w as the part of the principal’s wealth which can be easily observed and possibly

seized when an accident occurs.

The regulator maximizes a social welfare function which takes into account not only

the profits of the private sector, the budgetary cost of the regulatory scheme and the

cleanup cost or financial amount reimbursed to harmed third-parties. Following Laffont

and Tirole (1993), the regulator’s objective function can be expressed as:

W = U + V − (1 + λ)((1− e)D + ezn + (1− e)za),

where λ > 0 is the positive cost of public funds.10 For future reference, it is useful to

rewrite the regulator’s objective as:

W = (1 + λ) (Π− (1− e)D − ψ(e))− λ (U + V ) . (1)

This expression stresses the trade-off faced by the regulator in designing an optimal reg-

ulation. On the one hand, an efficient level of care maximizes the first bracketed term.

On the other hand, inducing such level of effort under moral hazard may require leaving

a rent U + V to the private sector. This rent is costly when λ is positive. This trade-

off distinguishes our analysis from the previous literature11 which assumes that rents in

the private sector are socially costless. Assuming that rents are socially costly allows us

to stress how different contracting modes affect this social cost and to characterize how

distortions in the level of care depend on the contracting environment.

Full Control: As a benchmark, let us suppose that both the effort e and the private

transaction (yn, ya) can be observed and regulated. The regulator’s problem becomes:

(R∗) : max{e,U,V }

(1 + λ)(Π− (1− e)D − ψ(e))− λ(U + V )

10We could as well assume that harmed third-parties receive a weight γ in the regulator’s objectivefunction so that W = U + V − γ(1 − e)D − (1 + λ)(ezn + (1 − e)za). This alternative formulationcould be useful to capture the often-heard claim that environmental regulatory agencies and judges inenvironmental litigation put more emphasis on victims when γ > 1. This would clearly not change ourresults provided that D is replaced by D′ = γD

1+λ .11Pitchford (1995), Balkenborg (2001) and Lewis and Sappington (2001a).

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subject to constraints U ≥ 0 and V ≥ 0.

These two constraints ensure participation of the agent and the principal. At the com-

plete information optimum, these participation constraints are obviously binding and the

private sector withdraws no rent (U = V = 0) from its activity. The first-best effort level

e∗ is such that the marginal benefit of reducing the likelihood of an accident equals the

marginal cost of effort:

D = ψ′(e∗). (2)

To implement this outcome, the regulator can first impose the standard e∗; second, require

the principal to leave the whole surplus of the transaction to the agent by setting y∗a =

y∗n = Π; third, force a fixed regulatory payment z∗n = z∗a = −Π + ψ(e∗) to ensure that the

agent breaks even.

Of course, the regulator might not observe all the relevant variables needed to im-

plement this first-best outcome. Either the effort e or both the effort and the private

transaction (yn, ya) might not be observable and can only be indirectly controlled through

the regulatory scheme (zn, za) that the regulator imposes on the sole agent. The analysis

of these settings with limited control will be the purpose of the next sections.

3 Moral Hazard in Safety Care

Under moral hazard, neither the regulator nor the principal can observe the agent’s effort.

Nevertheless, the regulator has still enough instruments to regulate the private transac-

tion. In this complete regulation setting, the regulator can impose the payments made

by the principal to the agent for any realization of his environmental performance.

Maximizing his expected profit, the agent chooses an effort satisfying the following

moral hazard incentive constraint:

zn + yn − (za + ya) = ψ′(e). (3)

Using (3), the agent’s expected utility becomes:

U = e(zn + yn) + (1− e)(za + ya)− ψ(e) = R(e) + za + ya.

Following Laffont and Martimort (2002, Chapter 4), we will define the agent’s limited

liability rent as R(e) = eψ′(e) − ψ(e) which is increasing and convex in e (R′(e) =

eψ′′(e) > 0 and R′′(e) = eψ′′′(e) + ψ′′(e) > 0). Being cashless, the agent is protected by

limited liability in the damage state so that za + ya ≥ 0. Inducing the agent to undertake

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a level of safety care e requires thus to leave him a liability rent R(e). We must have:12,13

U ≥ R(e). (4)

The principal’s participation constraint is:

V = Π− eyn − (1− e)ya = Π + ezn + (1− e)za − ψ(e)− U ≥ 0. (5)

The principal’s liability constraint can be written as Π− ya ≥ −w or, using (5),

V ≥ −e(yn − ya)− w. (6)

Under moral hazard, the regulator’s problem becomes therefore:

(RSB) : max{e,U,V,za,zn}

(1 + λ)(Π− (1− e)D − ψ(e))− λ(U + V ),

subject to constraints (4) to (6).

We summarize this optimization in the next proposition.

Proposition 1 Assume that there is moral hazard on safety care but that the private

transaction can be regulated. The optimal regulatory policy induces a second-best effort

level eSB such that eSB < e∗ and:

D = ψ′(eSB) +λ

1 + λeSBψ′′(eSB). (7)

The principal’s limited liability constraint (6) can be satisfied at no cost by giving to

the agent all the surplus from his relationship with the principal whatever the agent’s

environmental performance, ySBn = ySBa = Π. The agent’s and the principal’s payoffs are

respectively USB = R(eSB) and V SB = 0.

12 For any e ≥ 0, R(e) ≥ 0 and the agent’s participation constraint is implied by (4). Had the agentowned assets of value l, (4) would have to be replaced by U ≥ R(e) − l. In that case, the participa-tion constraint may be binding for l large enough, meaning that the first-best level of care can still beimplemented at no cost. For intermediate levels of l, both the participation and the limited liabilityconstraints may be simultaneously binding. This leads to a constrained optimum where, despite makingzero profit, the agent no longer exerts the first-best effort. The number of relevant cases in the analysisis thus simplified by our assumption that the agent has no wealth.

13Our model could be easily modified when the cost of effort may be monetary. This alternativeassumption would capture the fact that investments in safety care are a component of the firm’s costswhich is not easily verifiable. The firm’s liability constraint is now za + ya ≥ ψ(e) and (4) becomesU ≥ R(e) = eψ′(e). We have R′(e) > R′(e) and the second-best effort is greater with a monetarydisutility. Intuitively, by reducing the effort, the regulator relaxes now also the firm’s liability constraint.Although expressions differ, insights are similar to those obtained with a non-monetary cost.

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Under moral hazard, the regulator faces a trade-off between inducing a level of effort

close to the first-best e∗ and giving a socially costly rent R(e∗) to the agent, the only way

of inducing this effort. Reducing the effort below the first-best e∗ reduces this rent.

Implementation: When the private transaction is regulated, the regulator extracts all

the principal’s profit. To this end, the regulator has several possibilities obtained by

combining the payments yn and ya so that, in expectation, the principal’s profit is zero.

One such combination is particularly attractive in view of the analysis of the next section.

When ySBn = ySBa = Π so that V SB = 0, everything happens as if the agent had full

bargaining power in transacting with the principal. Since this private transaction does

not depend on the agent’s environmental performances, it does not perturb the agent’s

incentives and the level of care depends only on the regulatory transfers.

With this implementation, the principal is actually quite passive and does not interfere

with risk management. There is thus a complete dichotomy between the design of the

private transaction and the provision of incentives for safety care to the agent. Since the

principal remains passive, his liability constraint plays no role whatsoever. In addition,

za = −π leaves a rent U = R(eSB)

to the agent.

Corollary 1 Assume that there is only moral hazard on safety care and that the private

transaction is regulated. Increasing the principal’s collectable wealth w has no value.

For further reference, we note that the power of the regulatory scheme in the full

control environment can be defined as :

zSBn − zSBa = ψ′(eSB) = D − λ

1 + λeSBψ′′(eSB) < D.

This incentive power is less than the size of the harm done because effort is distorted down-

wards below the first-best. In the next section, we will see how the power of regulatory

incentives changes when the private transaction is no longer regulated.

4 Non-Observable Private Transaction

In practice, environmental regulators do not have the expertise and the monitoring tech-

nology necessary to audit and control the full set of contracts involving the firm. Regu-

lators can certainly determinate whether a given firm threatens the environment with its

activities. However, they may find hard to ascertain the whole set of stakeholders (sup-

pliers, customers, lenders, etc..) who are bound by contracts with the firm, even though

these transactions may significantly affect the management of environmental risk.

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In such incomplete regulatory settings, only the agent can be targeted ex ante with

a regulatory scheme. This regulation can be supplemented by an ex post liability rule

which may impose a fine on the principal/agent pair in the event of a damage once the

involvement (be it direct or indirect) of the principal has been proved.14 Of course, if it

is large enough, this fine ends up being paid by the wealthy principal since the agent is

cashless and the payments he gets from contracting may not suffice to pay the fine.

An incomplete regulation might restore some role for the principal’s wealth. The

results below on the benefits of extending liability can thus be interpreted as saying that

an incomplete ex ante regulation supplemented by an ex post liability rule sometimes

achieves what a complete ex ante regulation would have done.

To capture the fact that private transactions are not regulated, the relationship be-

tween the agent and his two masters (the regulator and the principal) is now modeled as

a common agency game under moral hazard along the lines of Bernheim and Whinston

(1986), with the special feature that the regulator remains a Stackelberg leader and that

the regulatory contract is publicly observable. The time line unfolds as follows:

-?

6

?

6

?

6

{zn, za} to the agent

The regulator offers

rewards and fines

The private transaction{yn, ya} is offered

both offersor refuses

The agent accepts

The agent chooseseffort e and produces

may occurAn accident

Regulatory transfersand payments

are realized

Figure 1: Timing with a non-observable transaction.

The agent must accept both contracts to produce since risk regulation is mandatory.

We solve for the Perfect Bayesian Equilibrium of that game by backward induction.

The design of the private transaction depends on the respective bargaining power of

the principal and the agent. For instance, lenders may have quite different bargaining

positions in negotiating loans with their borrowers. These principals may either compete

14The implicit assumption here is that, although it is prohibitively costly to determine ex ante thecontractual partners of the firm (because these contractual relationships might not even be alreadysigned), finding these partners ex post through litigation is not as costly.

11

head-to-head for the right to serve the agent or they may have developed close knitted

customer relationships which give them monopoly power with their clients.15 When the

project is financed by a parent firm which is in a unique relationship with its subsidiary

(maybe because some specific investments have already been sunk in the past), the prin-

cipal might have most of the bargaining power. We capture these different patterns in

the distribution of bargaining power by introducing a parameter α ∈ [0, 1] (resp. 1 − α)

which reflects the weight given to the principal (resp. the agent) at the contracting stage.

Note that the feasible regulatory payments za are necessarily bounded from below as

a result of both the agent’s and the principal’s limited liability constraints. Indeed, these

two liability constraints (respectively Π−ya ≥ −w and ya+za ≥ 0) altogether imply that

the following aggregate liability constraint of the principal/agent pair must hold:16

Π + za ≥ −w. (8)

To have a non-trivial continuation equilibrium of the game, fines should thus be small

enough so that this condition always holds. Intuitively, the maximum fine cannot exceed

the amount collectable from the principal/agent pair, i.e., the value of the transaction

plus the principal’s wealth. By increasing fines if an accident occurs, the regulator may

force the principal to increase the payment to the agent to keep him solvent. However,

doing so is only possible when the principal is himself wealthy enough.

Given that the principal has a bargaining weight α at the contracting stage, the optimal

private transaction solves:

(SPβ) : max{e,U,yn,ya}

(Π + ezn + (1− e)za − ψ(e)− U) + βU

subject to constraints (4) to (6),

where β = 1−αα

is the relative bargaining power of the agent. In solving (SPβ), we will

distinguish between the cases where either the agent (β ≥ 1) or the principal (β < 1) has

most of the bargaining power.

4.1 Dominant Agent

The solution to (SPβ) depends now on how large the fine is.

15See Sharpe (1990) and Rajan (1992) for models of relational banking developing this argument.16Reciprocally, when (8) holds, one can find ya such that both the principal’s and the agent’s liability

constraint hold. ya is then determined by the allocation of bargaining power in private contracting.

12

Lemma 1 Assume that the agent has most of the bargaining power in designing the pri-

vate transaction (β ≥ 1). The optimal transaction is such that the principal’s participation

constraint (6) is binding.

• Small fines: For −za ≤ Π, the effort is efficient from the point of view of the

principal/agent coalition:

zn − za = ψ′(e); (9)

• Large fines: For Π +w ≥ −za > Π, the effort is inefficiently low from the point of

view of the principal/agent coalition. It is uniquely defined by:

Π + za + e(zn − za − ψ′(e)) = 0. (10)

To understand the solution to (SPβ), it is useful to rewrite the principal’s participation

constraint (6) as:

Π + ezn + (1− e)za − ψ(e) ≥ U = R(e) + ya + za. (11)

This feasibility condition simply says that the whole surplus of the principal/agent coali-

tion (on the l.h.s.) must cover the limited liability rent of the agent (on the r.h.s.) plus

all transfers he receives from his two masters in the event of an accident. Constraint (11)

binds at the optimum of (SPβ) as soon as the agent has most of the bargaining power

and pushes therefore the principal down to his reservation value. Moreover, raising za

increases the right-hand side of (11) and hardens this constraint.

Think first of the case of a small fine which is less than Π. Since the agent has

most of the bargaining power, he pockets all that surplus and can thus pay the fine by

himself. This is akin to a regime where only the agent is under the threat of liability. All

the principal’s profit is extracted with a flat contract such that yn = ya = Π, and the

agent’s own limited liability constraint is still satisfied because za + Π > 0. The agent’s

private incentives to exert effort are aligned with those of the principal/agent pair as a

whole. Moral hazard does not affect private contracting. Condition (9) says then that the

marginal cost of effort equals its marginal benefit for the principal/agent coalition. The

effort is efficient from this coalition’s viewpoint.

If the fine −za is too large, this flat contract no longer works. The principal’s wealth is

now needed to pay the fine and we are in a regime of extended liability.17 To break-even,

the principal must then recoup this liability payment by diminishing the payment left to

17One can again use the Equivalence Principle here. Consider simply that the agent pays himself thefine but requests a higher payment ya to avoid bankruptcy.

13

the agent following a good environmental performance. For such a large fine, the agent’s

limited liability creates some perverse incentives since yn < ya. From (3), the agent’s

effort is below its efficient level from this coalition’s viewpoint.

4.2 Dominant Principal

Lemma 2 Assume that the principal has most of the bargaining power in private con-

tracting (β ∈ (0, 1)). The optimal private transaction induces a level of safety care e which

is lower than the efficient level from the principal/agent coalition’s viewpoint:

zn − za = ψ′(e) + (1− β)eψ′′(e). (12)

The agent obtains a rent U = R(e). The principal’s expected utility is:18

V = Π + za + (1− β)e2ψ′′(e) ≥ 0. (13)

Since the agent’s effort is not observed by the principal, the principal must give him a

liability rent to induce some positive effort. However, this rent is costly when β ∈ (0, 1)

and the cost increases as more of the bargaining power goes to the principal.

Condition (12) characterizes an important trade-off. On the one hand, efficiency within

the principal/agent coalition calls for choosing a level of effort such that the marginal

disutility of effort ψ′(e) is equal to the marginal benefit zn − za accruing to the coalition

as a whole. This efficient level of effort would be chosen if care were observable within the

coalition. On the other hand, inducing such a high level of effort requires giving more rent

to the agent. The marginal limited liability rent R′(e) = eψ′′(e) left to the agent adds up to

the marginal disutility of effort to assess the cost of marginally increasing effort within the

coalition. This limited liability term has to be weighted by the relative bargaining power

of the agent. In bilateral monopoly settings where β is close to one, the private transaction

maximizes the overall surplus and its distribution between the principal and the agent is

almost irrelevant. The effort level is then almost efficient. Starting from this benchmark,

the agent’s rent is viewed as more costly within the coalition and effort distortions due to

private contracting are increased as the agent’s bargaining weight decreases.

Using (3) and (12), we immediately get:

yn − ya = −(1− β)eψ′′(e) < 0. (14)

18Condition (13) requires that za cannot be too negative. Otherwise the principal prefers not to signany contract.

14

It could seem quite surprising that the principal reduces the agent’s payment following a

good environmental performance. The private transaction somewhat countervails regu-

latory incentives. Indeed, since some rent has to be left to the agent by a principal who

cannot observe the agent’s effort, the principal offers a marginal contribution yn − ya to

reduce the likelihood of a damage which is less than what it is worth to him. So doing

reduces effort and thus the liability rent of the agent. Since the principal does not value

per se a good environmental performance, the marginal contribution is negative.19

This contract increases the probability of an accident compared with the flat scheme

derived when transactions are regulated. Harmed third-parties could initiate litigation to

denounce this contract as providing incentives for reducing care if this contract was ob-

servable. Those contracts could thus be viewed as being criminal acts. That could trigger

further sanctions for the principal, most noticeably non-pecuniary ones like imprisonment

and the associated reputation loss. However, providing evidences that such a contract is

criminal is not as clear as it appears. Suppose indeed that the principal receives Π + ∆

(where ∆ > 0) in states positively correlated with a bad environmental performance.20

Then, the fact that ya is greater than yn might reflect only the existing incentives for

improving gains from trade. It may be hard to disentangle this incentive effect from the

desire of the principal to dilute regulatory incentives. The private transaction can then

hardly be viewed as being criminal.

In our context, the non-observability of the transaction countervails incentives for care.

The general idea here is that part of the regulatory incentives is diluted when private

transactions remain unregulated. Indeed, because of their common desire to extract the

agent’s liability rent, both the regulator and the principal create a wedge between their

marginal benefit of increasing the agent’s effort and the marginal cost of doing so. When

the principal considers modifying his transaction with the agent to extract his rent, he

does not take into account the impact of his decision on social welfare as a whole but

only on his own profit. Hence, there is a negative externality between both masters of

the firm. This leads to too little effort in equilibrium. Adding up agency costs in each

bilateral relationship in which the agent is involved will exacerbate distortions when both

the agent and the principal are cash-constrained as we will see below.21

19The principal could also suffer from a loss L in the event of an accident. This loss could be due tothe fact that assets are specific and have thus a lower resale value following the agent’s bankruptcy. Itmay also come from the fact that an accident may disrupt the production process and reduce the returnon investment expected by the principal. The results would then be slightly different although similarin spirit. Indeed, (14) would be replaced by yn − ya = L− (1− β)eψ′′(e) < L. The agent may receive agreater payment when there is no accident although the power of incentives of this private transaction isstill less than L, i.e., less than the principal’s valuation for avoiding an accident.

20This may be the case if the agent’s care is a substitute for his cost-reducing effort.21This negative externality reminds of the double marginalization distortions that arises when two

monopolists sell complement goods and do not coordinate their prices (see Tirole (1988, Chapter 4)).

15

4.3 Regulatory Response

Perverse incentives due to private contracting always arise whatever the allocation of

bargaining power. When the agent is dominant, they might come from the principal’s

desire to recoup the liability payment so that he can break even. When the principal is

dominant, those incentives come from his desire to extract liability rent from the agent.

Whatever this allocation, the regulator must undo these countervailing incentives or, at

worst, limit their impact. To show how this can be done, let us move backwards and find

the optimal regulatory scheme. Given the continuation of the game described above, the

regulator’s problem is now:

(R) : max{e,U,V,za,zn}

(1 + λ)(Π− (1− e)D − ψ(e))− λ(U + V )

subject to constraints (4), (8) and either (11) or (13),

where (8) and (11)/(13) are respectively the principal’s limited liability and participation

constraints once the outcome of private contracting is taken into account.22

4.3.1 Dominant Agent

Proposition 2 Assume that the agent has most of the bargaining power (β ≥ 1). The

optimal regulation still implements the second-best outcome with effort eSB and leaves to

the agent and the principal the rents USB = R(eSB) and V SB = 0.

When the transaction cannot be regulated, the regulator faces a double incentive

problem. First, he must induce the correct level of care from the agent, typically the level

found in Proposition 1. Second, he must induce the choice of a private transaction which

has no impact on care. If the agent has most of the bargaining power, the regulator can

easily achieve this outcome. First, remember that the regulator also wants to extract,

even though it is indirectly, the principal’s profit. When he is dominant, the agent is very

well suited to do so on the regulator’s behalf. Provided that the fine is not too large, the

agent remains solvent and his private incentives to exert care are not modified by private

contracting. There is no extra agency cost induced by private contracting. Implementing

a given level of effort costs the same as if the transaction could be regulated.

Implementation: This outcome is easily implemented with the regulatory transfers

zCa = −Π and zCn = −Π + ψ′(eSB). Then, the agent’s extracts all the principal’s rent in

22The principal’s participation constraint takes different expressions depending on whether he is dom-inant or not.

16

each state of nature yCa = yCn = Π. With this scheme, the regulator puts the principal-

agent coalition in the range of small fines. ¿From Lemma 1, moral hazard within the

coalition is then costless. This avoids any extra effort distortion due to private contracting

under moral hazard. The second-best outcome can still be implemented.

4.3.2 Dominant Principal

For future references, we define the third-best level of care eTB as:

D = ψ′(eTB) +λ

1 + λ((3− β)eTBψ′′(eTB) + (1− β)(eTB)2ψ′′′(eTB)), (15)

and the wealth levels w = (1 − β)(eTB)2ψ′′(eTB) and w = (1 − β)(eSB)2ψ′′(eSB). Note

that eTB < eSB and w < w since x2ψ′′(x) is an increasing function of x.

Proposition 3 Assume that the principal has most of the bargaining power (β ∈ (0, 1]).

Three possible regulatory regimes may arise depending on the principal’s wealth.

• Shallow pocket: When w < w, the optimal regulation implements the third-best

level of effort eTB which is strictly less than eSB.

The principal’s limited liability constraint is binding and the principal gets a strictly

positive payoff V TB = (1−β)(eTB)2ψ′′(eTB)−w > 0. The agent gets UTB = R(eTB).

• Intermediate pockets: When w ∈ [w, w], the optimal regulation implements a

constrained level of effort eC defined by:

w = (1− β)(eC)2ψ′′(eC). (16)

The effort eC increases with w and describes the whole interval [eTB, eSB] as w varies

in [w, w].

The principal’s participation and limited liability constraints are both binding and

the principal gets zero expected payoff V C = 0. The agent gets a rent UC = R(eC).

• Deep pockets: When w > w, the optimal regulation implements the second-best

level of effort eSB.

The principal’s limited liability constraint is slack and the principal gets zero expected

payoff. The agent gets a rent USB = R(eSB).

Implementing the second-best outcome is more difficult with a dominant principal

than with a dominant agent. To see that, consider the extreme case where the principal

has in fact all bargaining power (β = 0).

17

If regulatory transfers were directly targeted to the principal, standard moral hazard

theory teaches us that the risk-neutral principal could be made residual claimant for the

impact of any private transaction on the environment.23 As long as it would not violate

the principal’s liability constraint, this implicit delegation of the regulatory authority to

the private sector would be costless.

A first difference between this ideal setting and ours comes from the fact that, when

the transaction is not regulated, only the agent receives regulatory rewards. Following

the logic of the Equivalence Principle, this is only a minor difference since the private

transaction can redistribute transfers between the principal and the agent. An indirect

perfect delegation is therefore still possible when the principal is wealthy enough. To do

so, the regulator must simultaneously align the principal’s incentives to induce effort with

the socially optimal ones and extract (although indirectly through the regulatory scheme

imposed on the agent) his profit. Aligning incentives requires modifying the regulatory

scheme to undo the dilution of incentives which arises under private contracting. The new

regulatory scheme must be sufficiently high-powered so that, despite the countervailing

power of the private transaction, the agent ends up exerting the same second-best effort

as if the transaction was regulated. This requires that the principal bears more risk. In

particular, the fine in the event of an accident increases and the principal may be himself

insolvent if his wealth is small.

When he is cash-constrained, the principal must receive a rent to implement the proper

transaction. This is again socially costly. The regulator must distort incentives to reduce

this extra agency cost. This compounding of agency costs along the principal/agent

hierarchy requires to distort care below its second-best level.

Implementation: For a given bargaining power tilted in favor of the principal, let us

see in more details how the second-best outcome can still be implemented.

First, inducing eSB requires that the new regulatory scheme (zTBn , zTBa ) now offered

by the regulator satisfies:

zTBn − zTBa = D +

(1− β − λ

1 + λ

)eSBψ′′(eSB) > zSBn − zSBa . (17)

Indeed, taking into account the countervailing incentives as defined in (14), private con-

tracting induces the agent to choose an effort level which satisfies:

ψ′(e) + (1− β)eψ′′(e) = zTBn − zTBa . (18)

This equation admits a unique solution e = eSB.

Since part of the incentives are dissipated through private contracting, the socially

optimal level of care eSB can only be obtained if the regulatory scheme is higher powered23See Laffont and Martimort (2002, Chapter 4) for instance.

18

than when transactions are observable. The incentive power zTBn − zTBa may now exceed

D (at least when β is small) and the optimal policy then relies on punitive fines.24

Second, to extract the whole principal’s expected benefit from contracting, the regu-

lator must set rewards and fines so that:

V = Π + zTBa + eSB(zTBn − zTBa − ψ′(eSB)) = 0. (19)

Solving the system (17) and (19) gives the values zTBn and zTBa used by the regulator to

implicitly and costlessly delegate regulatory authority to the principal. Those expressions

show that the fine −zTBa has to be sufficiently large to do so. Such a fine will conflict with

the aggregate limited liability constraint (8) when the principal is not wealthy enough.

We also see on (17) that the incentive power of the regulatory contract(zTBn , zTBa

)increases as 1− β increases or as λ decreases. Punitive fines are less attractive when the

principal’s bargaining power diminishes because the countervailing power of the private

transaction itself diminishes. Also, when the social cost of the agent’s rent is small enough

and eSB is close to the first-best e∗, the regulation must be more punitive to undo the

significant dilution of incentives coming from the private transaction.

The above analysis shows the practical importance of imposing cash requirements

on stakeholders contracting with the firm. In practice, regulatory policies have often

similar features. For instance, various rules are imposed on stakeholders to demonstrate

financial responsibility. This has been the case for RCRA since an amendment passed in

1984 imposed that underground storage tank owners hold liabilities or purchase liability

insurance from third-parties to compensate victims in an amount up to 1 million US

dollars. As shown in our analysis, this kind of policies guarantees that the owner/operator

hierarchy fully internalizes the costs of storage tank hazards so that an efficient level

of prevention is performed even in the case of an incomplete environmental regulation.

Finally, the compensations for the victims of oil spills come from an international fund25

financed by oil companies upon request of the member States. The decisions of these

States to increase the required contributions of oil companies following the Prestige 2002

accident has often been viewed as providing incentives to these companies for better

delegating oil transport to the safer shippers.

4.4 A Useful Analogy

Consider the case where the principal has all bargaining power. To understand how the

liability rents of the agent and the principal compound, it is useful to see their coalition24According to Shavell (2004), “it is conventional to refer to damages that are greater than losses as

punitive”.25The International Oil Pollution Compensation Funds.

19

as a merged agent who, once the agency problem within the coalition is already solved,

behaves as having a virtual utility function given by:

Π + za + e(zn − za)− ψ(e)−R(e).

In terms of its safety care choice, this coalition has a virtual disutility of effort φ(e) =

ψ(e) + R(e) = eψ′(e). The corresponding virtual liability rent that must be given up by

the regulator to this coalition to induce an effort e is thus:

R(e) = eφ′(e)− φ(e) = e2ψ′′(e).

This virtual liability rent is precisely the rent that must be taken from the principal to

be sure that it is costless to delegate regulatory authority to the private sector. The

principal must be able to post ex ante a bond equal to this virtual rent for a costless

delegation of the regulatory authority to take place. If the principal cannot post such a

bond, distortions arise.

Recasting the results of Propositions 2 and 3: when w ≥ w = R(eSB), the principal

is wealthy enough to post this bond; when w > w > R(eTB) = w, we have a constrained

regime where effort is distorted but positively linked to the principal’s wealth w; lastly,

when w ≤ w, a liability rent must be given up to the principal.

4.5 Bargaining Power and Liability

We investigate now the relationship between the principal’s wealth needed to achieve the

second-best outcome even under an incomplete regulation and the allocation of bargaining

power. We already know from Proposition 3 that, for a given allocation, there is a positive

relationship between the principal’s wealth and the level of care. When the principal has

most of the bargaining power but is cash-constrained, an increase in the amount collectable

for damages relaxes his binding liability constraint and improves strictly welfare. This

better aligns the principal’s private incentives to induce care with the socially optimal

ones. It also strictly increases the level of care when w lies in the interval [w, w] since

effort is positively linked to the available wealth when the principal has an “intermediate”

pocket. In this case, full extraction of the principal’s rent is still possible, but obtained

at the cost of decreasing the effort below the second-best level.

Let us now fix the principal’s wealth and vary his bargaining power within the coalition.

Corollary 2 There exists β∗(w) = max{0, 1 − w(eSB)2ψ′′(eSB)

} < 1 such that, for β ≥β∗(w), the second-best regulation can be implemented even under an incomplete regulation.

Extending the principal’s liability by raising w has no value.

20

By increasing the principal’s wealth collectable for damages, one weakens the princi-

pal’s bargaining position vis a vis the agent. Indeed, even when the principal is dominant,

the regulator can raise fines up to the point where the principal has to leave most of the

surplus from the transaction to avoid the agent’s bankruptcy; exactly as if the principal

had less bargaining power. The principal’s liability can thus be viewed as a substitute for

his own bargaining power.26

As λ diminishes, eSB increases towards the first-best level e∗ and thus β∗(w) also

increases. When the social cost of the rent diminishes, the punitive content of regulatory

schemes must increase since the countervailing power of the private transaction is more

significant, as it can be seen from the r.h.s. of (14) which decreases with e. For a given

allocation of bargaining power, it becomes more valuable to increase the collectable wealth

to raise welfare.

¿From a policy perspective, it is important to stress a few cases where extended liability

may certainly be beneficial. Financiers who have developed a unique relationship with

firms are the best targets for that policy. Also, extended liability may be particularly

useful in transportation where agents are highly competitive.

5 Extensions

5.1 Affiliated Principals

On top of the polar cases where principals are fully competitive and where they hold a

monopoly position vis-a-vis their agent, there is a whole range of possible organizational

structures where a single agent deals in fact with several principals without having bar-

gaining power with any of them. Boyd and Ingberman (2001) coined the expression of

affiliated principals to characterize such settings. For instance, one may think of those

principals as n (n ≥ 2) different lenders bringing each a fraction In

of the overall invest-

ment of the firm. Those principals could also be n polluting contractors affiliated via the

firm which disposes or transports pollutants on their behalf.

Although such settings seem at first glance akin to a reduction of each principal’s bar-

gaining power vis-a-vis the agent, one has to be cautious in generalizing the predictions of

the one-principal model. Indeed, implementing the second-best outcome with an incom-

plete regulation cum liability rules requires now to make each of these principals residual

26Note that extending the principal’s liability may still be irrelevant when the principal has most ofthe bargaining power but the distribution of bargaining power is quite even (β close to 1 from below).The principal’s liability constraint is then automatically satisfied when his participation constraint holds.Also, when the principal’s bargaining power is small enough, extending liability is irrelevant since thesecond-best outcome can already be achieved by regulating only the agent.

21

claimant for the harm done. Far from facilitating this implementation, the presence of

multiple stakeholders makes it more difficult. We characterize below the bound on the

principals’ aggregate wealth which is now needed to implement the second-best outcome

and show that it increases with the number of principals.

To make things simpler, we assume that principals are symmetric. Each pockets Πn

of

the gains from trade and holds assets worth wn

.27

Let us denote by (yin, yia) the contract offered by principal i (i ∈ {1, .., n}). The agent’s

incentive constraint can now be written as:

zn +n∑i=1

yin − (za +n∑i=1

yia) = ψ′(e); (20)

and his limited liability constraint as:

za +n∑i=1

yia ≥ 0. (21)

For a given regulatory scheme, the Nash equilibrium in contracts among the n non-

cooperating principals leads to an effort level given by:28

zn − za = ψ′(e) + neψ′′(e). (22)

In this non-cooperative setting, a given principal does not take into account the impact of

his own desire to reduce the rent of the agent on the surplus of the bilateral relationships

involving this agent with other principals. Each principal individually countervails the

regulatory incentives and sets a negative marginal reward:

yin − yia = −eψ′′(e) < 0. (23)

Just like in the single principal case, each principal chooses a bilateral contract with

the agent with an incentive power which is his own marginal valuation for the agent’s

effort (here again zero because principals do not care directly about a damage) minus

the marginal cost of the agent’s rent. As those distortions add up in a non-cooperative

equilibrium, there is an excessive reduction of the agent’s rent. The agent’s effort ends

up being significantly downward distorted below the effort that would be obtained had

principals jointly designed his incentives. There is free-riding among the principals over

27Boyd and Ingberman (2001) argue that, because liability on affiliated contractors is joint and several,asymmetric principals will not be affiliated altogether. According to these authors, the threat thatwealthy principals have to subsidize shallow-pocket ones in the event of a damage makes them separatefrom each other, so that affiliated structures should form with principals having comparable wealth.

28See the Appendix for details. For simplicity, we assume that the n principals are needed so that wemodel a game of intrinsic common agency. This is for instance the case if each principal is a lender whofaces a capacity constraint and can only finance a fraction 1

n of the project.

22

the provision of incentives to the agent. Affiliation of the principals thus worsens the

countervailing effect of private transactions on regulatory incentives.

Let us assume that liability is joint and several29 so that symmetric principals end up

sharing equally fines in the event of an accident. Each principal gets a profit worth:

V =Π + zan

+ e2ψ′′(e) ≥ 0. (24)

Without embarking on a full-fledged analysis similar to Section 4, let us determine

the conditions under which delegation of the regulatory authority to the private sector is

costless and what happens when, instead, the liability constraint of each principal binds.

To implement the second-best outcome eSB, the regulator must now undo the severe

dilution of incentives that results from the principals’ non-cooperative behavior. This can

be done by offering a very high-powered regulatory scheme (zMn , zMa ) such that:30

zMn − zMa = D +

(n− λ

1 + λ

)eSBψ′′(eSB) > zTBn − zTBa . (25)

The regulatory policy is more punitive with affiliated principals than with a single stake-

holder and the punitive content increases with the number of principals involved.

To extract each principal’s profit without hitting his liability constraint, we must have:

−zMa = Π + n(eSB)2ψ′′(eSB) < Π + w. (26)

This r.h.s inequality is more stringent as n increases. It is more difficult to ensure cost-

less delegation of the regulatory authority as more principals contract with the agent.

Intuitively, a costless delegation requires now that each principal posts a bond equal to

the rent withdrawn from contracting independently with the agent. This bond is ex-

actly the virtual rent obtained by the merged entity that this principal forms with the

agent. With multiple principals, those rents add up and make it more difficult to sat-

isfy the aggregate liability constraint of the principals. The minimal aggregate wealth

w(n) = n(eSB)2ψ′′(eSB) above which delegation is costless increases linearly with n.

Let us now turn to the polar case where the limited liability constraint of each principal

is binding. To induce an effort e, each principal must now get a rent worth:

V = e2ψ′′(e)− w

n> 0. (27)

Using symmetry, the regulator’s problem becomes:

(RM) : max{e,U,V }

(1 + λ)(Π− (1− e)D − ψ(e))− λ(U + nV )

29One of the principals is then held liable for the whole damage caused by the agent and threatens then− 1 others with litigation to share equally the financial burden.

30Where the superscript M is meant for multiple principals.

23

subject to constraints (4) and (27).

The optimal effort level eM in this environment with affiliated principals becomes:

D = ψ′(eM) +λ

1 + λ((2n+ 1)eMψ′′(eM) + n(eM)2ψ′′′(eM)). (28)

Taking for instance the case where ψ(e) = e2

2and making the dependence of eM on n

explicit, we observe that eM(n) decreases with n due to free-riding among principals in

providing incentives to the agent. The liability constraint of each principal is now binding

when:

w < w(n) = n(eM(n))2 =nD2(

1 + λ1+λ

(2n+ 1))2 . (29)

It is easy to check that w(n) is inversely U-shaped in n. There are two effects at work

here. First, as we saw above, the aggregate wealth of the principals must be lower than

n times the rent obtained by each of them from his relationship with the agent in order

to create a liability problem. This first effect tends to increase the bound w(n). Second,

as more principals get involved, the equilibrium effort of the agent diminishes because

of free-riding and the rent that each principal gets from his relationship with the agent

decreases. This makes it somewhat harder to satisfy (29) so that principals are less likely

to have a shallow pocket. This second effect dominates for n large enough. As a result of

those two effects, w(n) achieves its maximum at n = 3 when the cost of public funds λ is

close to .3, a value commonly accepted. Principals find it easier to be shallow-pocketed

and thus to earn a positive liability rent in affiliated structures involving such a small

number of principals. Exactly as principals may reduce the size of their collectable wealth

to escape liability payments and earn a liability rent, they may also choose to be affiliated

with only a few other principals.31

5.2 Ban on Regulatory Rewards

In the U.S., the statutory ability of environmental agencies for using transfers with regu-

lated firms (both at the Federal and at the State levels) is often more limited than assumed

so far. Although fines are feasible, financial rewards for good environmental performances

may not always be authorized.32 This extra incompleteness of the regulatory scheme puts

certainly some constraints on the delegation of regulatory objectives to the private sector.

Sticking to this real world institutional setting amounts to forcing zn = 0.

31For w ∈ [w(n), w(n)], the effort level is constrained by the principals’ limited wealth. The constrainedeffort level eC(n) decreases with n and solves now neC(n)ψ′′(eC(n)) = w. For those principals withintermediate pockets, raising their collectable wealth increases again welfare and effort.

32However, indirect rewards from good environmental performances can still be present as we arguedwhile presenting the model in Section 2.

24

Let us first consider the case of a dominant agent which has attracted much of the

attention in the literature.33 First, it may be that Π ≥ ψ′(eSB) if the second-best effort

eSB is sufficiently distorted below the first-best e∗ even if the level of harm D is much

greater than Π.34 There is a simple way for the regulator to implement the second-best

level of effort eSB even in the absence of rewards. Suppose that the regulator imposes

a fine −zSBa = ψ′(eSB). The agent having all bargaining power offers a flat contract to

the principal ya = yn = Π which extracts all surplus from the transaction and does not

perturb incentives. The surplus pocketed by the agent is enough to cover the fine and the

agent chooses the second-best level of effort.

Suppose now that Π < ψ′(eSB). By choosing the fine −zWa = Π, the regulator can

implement a level of effort eW such that Π = ψ′(eW ). Note that eW < eSB so that, by

concavity of welfare in e, raising effort above eW would improve welfare. Can the regulator

improve on this outcome? Raising the fine may a priori foster care but it requires also

using the principal’s wealth and this introduces countervailing incentives. From Lemma

1, the effort level is indeed given by the principal’s zero profit condition. This condition

can be rewritten taking into account the ban on rewards as:

Π + (1− e)za − eψ′(e) = 0. (30)

This expression defines the fine as a function of the effort level implemented −za =

H(e) = Π−eψ′(e)1−e . Differentiating with respect to e, we find H ′(e) = Π−ψ′(e)−e(1−e)ψ′(e)

(1−e)2 and

thus H ′(eW ) < 0. Therefore, raising the fine above Π decreases the effort level below eW

and reduces also welfare. We recover here Pitchford (1995)’s result that extended liability

may be costly when the principal has no bargaining power. His result extends thus to the

second-best environment considered in our paper.

Consider now the case of a dominant principal and for simplicity assume that he has

all bargaining power (β = 0). Taking into account the ban on rewards and using Lemma

2, the effort satisfies:

−za = ψ′(e) + eψ′′(e). (31)

Using (1) and setting zn = 0, the regulator’s problem can now be written as:

(RL) : max{e,za}

Π− ψ(e)− (1 + λ)(1− e)D − λza(1− e)

subject to constraints (8), (13) and (31).

33See Pitchford (1995, 2001) and Lewis and Sappington (2001a) for instance.34Even if the cost of public funds λ is close to zero, a very convex disutility of effort (ψ′′(·) large) is

enough to guarantee that this case is relevant. This case never arises in the analysis of Pitchford (1995)because the second-best level of effort remains equal to the first-best when λ = 0.

25

The fine −za plays now two roles at the same time: first, inducing effort and, second,

shifting rents away from the private sector since those rents are costly when λ > 0.

When Π and w are small enough, the optimal effort eW is obtained by using (31) and

binding (8):

Π + w = ψ′(eW ) + eWψ′′(eW ). (32)

Raising the principal’s liability w increases the level of care and improves welfare.

6 Conclusion

Extending liability towards principals linked through contracts with an agent involved

in environmentally risky activities may improve welfare when private contracts cannot

be regulated. Even with such incomplete regulation, the management of environmental

risk can in fact be indirectly delegated to the private sector but it requires increasing

fines and rewards. This is of course easier when part of these large ex post fines are

paid by principals. Otherwise, the optimal regulation may take into account an extra

agency cost of delegation and calls for strong distortions in the level of precautionary care

undertaken by the agent. Increasing the wealth of principals that can be collected helps

thus improving this implicit delegation and moves the level of care towards the second-

best level. This result holds under a broad range of possible values of the principal’s

bargaining power but also for more complex organizations involving multiple principals

jointly contracting with the agent or when regulatory rewards are banned.

The fact that rewards and fines are increased under an incomplete regulation gives

significant discretionary power to regulators and thus increases the scope for capture.35

One possible response to this threat of capture is to limit the regulator’s discretion by

reducing either punishments or rewards. In the first case, extending liability may then be

less attractive. In the second case, banning rewards in the event of good environmental

performances still leaves some scope for extending liability as shown above. A second

possible response to the threat of capture is to separate ex ante regulation from ex post

litigation. In our model, the two aspects of risk control have been merged and viewed

as a single incentive contract offered by a merged entity. Hiriart, Martimort and Pouyet

(2005a) give a more active role to regulators and judges by allowing them to monitor care

either ex ante or ex post. They show that splitting these monitoring tasks helps reducing

the threat of capture.

35It is indeed well known that high-powered incentive schemes may be particularly prone to regulatorycapture. See Laffont and Tirole (1993, Chapter 11). On this issue of capture, see Boyer and Porrini(2004) who compare a captured regulation with an uncorruptible liability regime.

26

Another assumption that should be relaxed is the fact that the regulator knows the size

of the principals’ wealth. Because principals may hide assets in various ways, asymmetric

information on wealth may arise. The implicit delegation of regulatory authority to the

private sector becomes more difficult because it is not known whether principals have

enough assets to manage risk efficiently.36 To the agency costs of moral hazard, one must

now add also the rent that wealthy principals may withdraw from their assets hiding.

This may tighten the bound on wealth above which the implicit delegation of regulatory

authority to the private sector is costless and make extended liability less attractive. On

the other hand, asymmetric information on wealth requires to develop a whole legal arsenal

to unveil assets. Extending liability through a legal procedure may be quite attractive in

this respect.37

It would also be worth introducing into our framework a substitutability between care

and cost minimizing effort.38 Increasing care raises cost and reduces thereby the gains

from trade with the principal. This countervailing effect might certainly influence the

kind of contracts signed with principals. Principals may want to write contracts which

induce even more countervailing incentives for the agent compared to our setting which

does not include such substitutability in efforts. This effect should reinforce our previous

findings. When principals have most of the bargaining power, the regulator should design

an ex ante regulatory contract with even higher-powered incentives. Indeed, the regulator

must now undo not only the desire of principals to extract the firm’s liability rent but

also their desire to divert the firm’s effort towards more productive activities. These are

issues that we plan to explore in future works.

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Appendices

• Proof of Proposition 1: The proof is straightforward: we first find the optimal effort

neglecting constraint (6) and then, we check that there exists values of (yn, ya) which

satisfy (6).

29

First step. The regulator wants to reduce U and V as much as possible since λ > 0.

Both (4) and (5) are thus binding. Inserting U = R(e) into the objective function which

becomes a strictly concave function of e and optimizing, we find (7).

Second step. To satisfy (6), one possibility (among others) is to set ySBn = ySBa = Π.

With those values, the moral hazard constraint (3) becomes:

zSBn − zSBa = ψ′(eSB) = D − λ

1 + λeSBψ′′(eSB) < D.

With the agent’s limited liability constraint ya + za ≥ 0 being binding, we finally obtain

zSBa = −ySBa = −Π and all transfers are defined.

• Proof of Corollary 1: Direct from the text.

• Proof of Lemma 1: First, we observe that (11) must be binding at the optimum when

the agent is dominant. This can be done by raising ya as long as (6) is satisfied, i.e., as

long as ya ≤ Π + w.

Two cases must be distinguished depending on whether the effort e which maximizes

the complete information total payoff of the coalition (such that ψ′(e) = zn− za), satisfies

(11) or not. This is the case when for this value of e:

Π + za + e(zn − za)− ψ(e) ≥ R(e) + ya + za,

or Π − ya ≥ 0. Of course, since the agent has most of the bargaining power, he chooses

ya = Π. Given that ya+za ≥ 0 must be satisfied, this case can only occur when −za ≤ Π,

i.e., for small fines.

When Π < −za ≤ Π + w, we are in the case of strong fines, the effort solution to

(SPα) is no longer interior and efficient, and is constrained by equation (11). Of course,

za must not be too negative otherwise the constrained set defined by (11) is empty. This

is ensured when

Π + za + e2∞ψ

′′(e∞) ≥ 0,

where e∞ is defined implicitly as

zn − za = ψ′(e∞) + e∞ψ′′(e∞).

Note that the regulator should not choose zn and za such that the constrained set of

(SPβ) is empty since then the market for private transactions would break down. When

the constrained set is non-empty, the optimal effort is obtained when ya + za = 0 and we

find that it solves (10). Note that zn − za = ψ′(e) − Π+zae

> ψ′(e). Hence the effort no

longer maximizes the complete information aggregrate payoff of the coalition.

30

• Proof of Lemma 2: We neglect (5) and (6) which will be satisfied with a convenient

choice of zn and za by the regulator. Of course, (4) must be binding since the agent’s

limited liability rent is privately costly for the principal. Hence, ya + za = 0. Inserting

U = R(e) into the principal’s objective which becomes strictly concave in e, we obtain

the first-order condition (12).

• Proof of Proposition 2: It is obvious to check that yn = ya = Π = −za maximizes

the agent’s expected utility, extracts the principal’s rent, and induces an effort e such that

ψ′(e) = zn − za. For zCn and zCa proposed in the text, eSB is chosen.

• Proof of Proposition 3: Let us first find the regime where only (8) is binding. Then,

V = (1 − β)e2ψ′′(e) − w and inserting this value into the regulator’s objective function

along with the other binding constraint (4) yields an objective function which is strictly

concave in e:

(1 + λ)(Π−D(1− e)− ψ(e))− λ(R(e) + (1− β)e2ψ′′(e)− w).

Optimizing with respect to e yields (15). This regime occurs as long as w < w.

Let us assume, on the contrary, that (13) is binding and (8) is slack. Then, since (4)

remains binding, the objective function of the regulator becomes:

(1 + λ)(Π−D(1− e)− ψ(e))− λR(e),

which is maximized for eSB. Since (e2ψ′′(e))′ > 0, it is straightforward to check that

eTB < eSB. This regime occurs as long as w > w.

Finally, for w ≥ w ≥ w, both (8) and (13) are binding and w = (1− β)e2ψ′′(e). As w

increases, the optimal effort describes the whole interval [eTB, eSB].

• Proof of Corollary 2: Direct from the text.

• Nash Equilibrium Among Principals: From (20), we get

U ≥ za +n∑j=1

yja +R(e) ≥ R(e), (33)

where the inequality follows from (21).

At a best response, principal i wants to solve:

(SP i) : max{e,U,}

Π + e

(zn +

∑j 6=i

yjn

)+ (1− e)

(za +

∑j 6=i

yja

)− ψ(e)− U

subject to (33).

31

The constraint is binding and thus, principal i wants to induce an effort level i such that

zn +∑j 6=i

yjn −

(za +

∑j 6=i

yja

)= ψ′(e) + eψ′′(e). (34)

Summing those equations for all i and taking into account (20) yields then (22). Finally,

using again (34), we get (23).

32